PSI - Issue 1

R.L. Fernandes et al. / Procedia Structural Integrity 1 (2016) 042–049 Fernandes and Campilho/ Structural Integrity Procedia 00 (2016) 000 – 000

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P [N]

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δ [mm]

δ [mm]

a) b) Fig. 5 – Comparison between the experimental P -  curves with the numerical predictions: Araldite ® AV138 (a) and Sikaforce ® 7752 (b). It was found that, for the Sikaforce ® 7752, the triangular and exponential CZM laws consistently under predicted the P values during crack growth comparatively to the experimental P -  curves. On the other hand, the trapezoidal law was accurate in capturing the experimental results. It is considered that this difference arises from the high ductility of this particular adhesive. In average, the percentile deviations between the experimental and numerical values of P max and  P max are the following: 2.16% and 3.44% (triangular CZM law), 3.14% e 6.07% (trapezoidal CZM law) and 12.21% and 3.37% (linear-exponential CZM law). In summary, for adhesives other than highly ductile, the crack growth behavior is not affected by the CZM law shape and, thus, any law is applicable, which reinforces the previously mentioned statement that in pure tension the strength predictions are practically independent of the CZM law shape. On the other hand, crack initiation in bonded structures is affected by the CZM law, with the linear-exponential law triggering premature failure, especially for ductile adhesives. This work initially aimed at evaluating G IC and the tensile CZM law of two structural adhesives with distinct ductility. This was accomplished by performing fracture tests on DCB specimens and using the J -integral/direct method. G IC was assessed by the steady-state values of G I in the respective G I -  n curve of each specimen, giving consistent values with the adhesive type and known behaviour from the literature. The obtained CZM laws showed a best fit of the Araldite ® AV138 with a triangular law, while the Sikaforce ® could be more accurately represented by a trapezoidal CZM law due to its ductility. The numerical simulations enabled a clear insight regarding the best CZM law shape to model the tensile behaviour of each adhesive in bonded joints. The propagation region in the P -  curves for the Araldite ® AV138 was not affected by the CZM shape, oppositely to what happened with Sikaforce ® 7752, in which the triangular and linear exponential CZM laws revealed to under predict P during crack growth. This discrepancy was associated to the large ductility of the adhesive. P max and  P max were also used as indications of approximation to the experiments. The absolute errors in these values were close between the triangular and trapezoidal laws for the Araldite ® AV138, while the linear-exponential CZM law resulted in excessive softening in the initial stages of damage and thus, bigger deviations in the results. The P max values were also highly under predicted with a linear-exponential CZM law. The general conclusion taken from this work is that, if the adhesive is not highly ductile, the adhesives’ behaviour during crack growth can be correctly modelled by any CZM law shape. On the other hand, crack initiation is anticipated by using linear-exponential CZM laws. Experimental Triangular Trapezoidal Exponential Experimental Triangular Trapezoidal Exponential 5. Conclusions

References

Li, J., Yan, Y., Zhang, T. and Liang, Z. 2015. Experimental study of adhesively bonded CFRP joints subjected to tensile loads. International Journal of Adhesion and Adhesives 57: 95-104. Ripling, E., Mostovoy, S. and Patrick, R. 1964. Application of fracture mechanics to adhesive joints. ASTM Special Technical Publication 360: 5 19. Floros, I. S., Tserpes, K. I. and Löbel, T. 2015. Mode-I, mode-II and mixed-mode I+II fracture behavior of composite bonded joints: Experimental characterization and numerical simulation. Composites Part B: Engineering 78: 459-468.